ORIGINAL PAPER

Understanding demand volatility in supply chains throughthe vibrations analogy—the onion supply case

Sanjay Sharma • Kamaldeep Singh Lote

Received: 3 October 2011 / Accepted: 25 June 2012 / Published online: 8 July 2012

� Springer-Verlag 2012

Abstract Fluctuating demand for goods in many situa-

tions is not caused by genuine discontinuities in the con-

sumption or usage of those goods. Basic food products, for

example, are consumed at relatively stable rates. But dis-

ruptions in their supply—real or imputed—may cause

demand volatility with consequences of unwanted price

fluctuations. In this paper, the vibrations analogy is pro-

posed to better understand this phenomenon. Various

alternative scenarios of damping vibrations are discussed in

this paper, viz., underdamped, overdamped, and critically

damped system. An interpretation of those scenarios is

offered with respect to their meaning to supply chain

management and illustrated through the case of the onion

supply. The proposed analogy is found to be useful in

explaining and taking appropriate steps for improvement in

such cases.

Keywords Supply chain � Vibrations analogy � Supply

disruption � Volatility � Damping � Onion supply

1 Agricultural supply chains and the promise

of an alternative analytical approach

In recent years, supply chain management has emerged

as one of the most important functions in business. From

oil rigs to onion farms, supply chains are now being con-

sidered as most critical for the successful integration

of business functions across the globe. Arshinder et al.

[1], De Treville et al. [7] and Vonderembse et al. [40]

have emphasized supply network designs, strategies and

practices as essential elements of business strategy in the

rapidly changing world of sourcing, production and

distribution.

A supply chain links a network of companies, forming

multiple tiers. In normal course, the customers are getting

their desired product on time, at appropriate price and in

sought quantities. But disruptions and delays occur at

times. Disruptions and delays have been discussed by

Chopra and Sodhi [4] among different categories of risk.

Dependence on fewer sources of supply [36] is considered

as one of the several drivers of disruption risk. Poor quality

or yield at supply source is mentioned as another potential

driver of risk. To support the process of value creation to

customers in complex supply chains, information needs to

be utilized and exchanged in buyer–supplier relationship

[12, 25, 26]. The more tightly coupled the business pro-

cesses are, the more the information sharing is required, as

studies in a manufacturing context have shown [31, 35, 37,

38, 41].

Flexibility of demand has been considered [29]. Phe-

nomena of unwanted supply chain fluctuations have also

been incorporated in a different line of research, that is, the

bullwhip effect and supply chain issues among others [5, 8,

13–15, 17, 22]. The objective of the present paper was not

to review the bullwhip effect and related research in detail.

This is because of certain significant differences of the

present analogy approach from the discussed stream. Par-

ticularly in the traditional bullwhip effect literature,

demand or order amplification is discussed as movement is

made toward upstream in the chain. Analysis may pertain

to the managerial discussion in a highly organized indus-

trial chain or modeling approach limited by the assump-

tions. The setting may also be limited by one firm in each

tier with two or more number of levels in the chain.

S. Sharma (&) � K. S. Lote

National Institute of Industrial Engineering (NITIE),

Vihar Lake, Mumbai 400087, India

e-mail: s_nsit@rediffmail.com

123

Logist. Res. (2013) 6:3–15

DOI 10.1007/s12159-012-0083-z

The present paper focuses on a real onion supply case

and tries to explain the happenings with the help of

vibrations analogy, although it has a reasonable scope for

generalization. To the best of our knowledge, this kind of

analogy has not been discussed precisely following the

vibration theory in the supply case scenarios including the

bullwhip effect literature. Additionally, we also incorporate

the supply chain structural issues. The proposed approach,

however, is also expected to contribute toward adding new

insights, particularly in terms of an interaction of supply

chain structure and bullwhip effect handling.

Most of the supply-chain-related work has been done in

an industrial context so far. But agricultural supply chains

have received less focus in the literature. This might be

because agricultural supply chains should be analyzed

depending on specific product and process characteristics

[39]. One illustrative case study has been presented by

Rong et al. [23], related to a specific agricultural product,

that is, the supply chain for bell peppers. Focus of these

authors is on controlling the fresh food quality throughout

the supply chain.

Key points associated with the difference between the

‘‘bullwhip effect studies’’ and the present study are as

follows:

• In traditional ‘‘bullwhip,’’ the stimulation comes from

changes in demand at the downstream end of the supply

chain; in the present case, the stimulation comes from

the upstream supply.

• In ‘‘bullwhip,’’ one-to-one single supplier links along

the supply chain are considered; in our case, situations

of smaller and larger numbers of potential suppliers at a

tier are also incorporated.

• In general, the discussions usually consider supply

chains in industrial contexts, that is, for ‘‘industrial-

ized’’ wholesaling and retailing; we look at agricultural

context considering a relevant case.

This paper suggests an analysis of the case of onion

supplies in India, applying a non-traditional approach. In

this case, focus on information sharing and the structure of

the supply chain are critical. It makes use of the analogy of

vibrations theory to study supply chain phenomena, fol-

lowing the suggestions by Schleifenbaum et al. [27]. Ka-

chani and Perakis [9] applied fluid dynamics models in

transportation and pricing. Romano [21] explained supply

chain issues with the help of fluid dynamics in the context

of clothing industry.

More specifically, this paper investigates how the

upstream disruptions in an agricultural supply chain cause

increased order volatility in the downstream sections of the

chain. It considers alternative approaches to dampen the

order volatility following supply chain disruption based on

the proposed vibration–supply chain analogy.

After a brief introduction to the food supply markets

in India, in its third section the paper mainly discusses

the basics of vibration theory and its relationship with

supply chain management. Three cases of ‘‘viscous

damping’’ are also explained. In Sect. 4 of the paper,

insights from the vibrations analogy are transferred to the

case of a recent supply crisis in the market for onions in

India, in order to illustrate the usefulness of the vibra-

tions analogy. These sections try to answer the following

questions:

i. What are the differences between various supply

chain situations?

ii. What are the critical parameters in a supply chain

scenario affecting its fluctuations/damping behavior?

iii. Which consequences for supply chain design and

management may be drawn from the vibrations

analogy analysis to better control fluctuations?

2 The market for onions in India

Agriculture is the source of livelihood to more than two-

thirds of India’s population and contributing approxi-

mately 20 % to the gross domestic product (GDP) of

India. Thus, agriculture holds a prominent position as an

occupation for the common Indians. Agricultural com-

modity exports contribute nearly 20 % of the total export

earnings of the country. Onion, tomato and mushroom are

highly export competitive among fresh vegetables. India

ranks first in the world accounting for around 21 percent

of the world area, in which onion is planted. Globally, the

country occupies the second position, after China, in

onion production, with a production share of around 14

percent. Besides India and China, the other major onion-

producing countries are Turkey, Pakistan, Iran, Japan,

Brazil, United States of America and Spain. Onion is

produced for both domestic consumption and exports.

India produces all varieties of onion—pink, red, yellow

and white, big or small [19].

Onion is an elementary part of the diet in India. A

common man in India spends more than 43 % of his dis-

posable income on food items (PHDCCI 2011) [18]. Thus,

any substantial increase in food prices may lead to certain

effect on monthly budget. This case discusses the onion

crisis faced during the last quarter of the year 2010 and in

the beginning of 2011.

In India, onion is extensively cultivated in all seasons

over a large area spread almost throughout the country.

However, Karnataka, Maharashtra and Gujarat are the

major onion-producing states accounting for about 60 % of

the area and production of onion in the country. According

to the National Horticulture Board (India), Maharashtra is

4 Logist. Res. (2013) 6:3–15

123

the largest onion-producing state accounting almost one-

fourth of total production of the country.

Figure 1 clearly depicts that Maharashtra leads in pro-

duction (21 %) of onion in the country. Thus, we have

chosen Maharashtra as one of the states for our study on

onion crisis to understand more clearly how the supply

shortage may lead to order variation and subsequent inef-

ficient damping.

According to the National Horticulture Research and

Development Foundation (India), diseases caused by un-

seasonal rains ruined almost 70 percent of the ‘‘Kharif’’

(corresponding to the period under consideration) onion

crop in Maharashtra in the year 2010, which was respon-

sible for the nationwide shortage of the commodity. This

led to a sharp fall in output in the state—the largest pro-

ducer of the commodity in the country—which in turn

resulted in sky-high prices across the country. Existing

market players virtually block the entry of new players,

which led to practices such as cartelization and hoarding.

Apart from this, the inadequacy of supply chain infra-

structure added woes to the common man. In this way, the

major causes for increase in prices can be identified as

follows:

(i) Unseasonal rains

(ii) Practices such as cartelization and hoarding

(iii) Inadequate supply chain infrastructure

In this paper, the inadequacy of supply chain infra-

structure to dampen the price and demand volatility is

being discussed in detail using the supply chain–vibrations

analogy.

3 Introducing the vibrations analogy

Efficiency of supply chains mostly depends on manage-

ment decisions, which are often based on intuition and

experience. Different stages in supply chains are often

supervised by different groups of people with different

managing philosophies, which sometimes create problems.

Sarimveis et al. [24] also laid emphasis on rigorous

framework for analyzing the dynamics of supply chains

Fig. 1 Onion production in Indian states

Logist. Res. (2013) 6:3–15 5

123

and taking proper decisions to significantly improve the

performance of the systems. In order to better understand

supply chain phenomena, several analogies have been

proposed for their analysis, such as fluid mechanics and

supply chain analogy by Romano [21] and control theory

analogy by Dejonckheere et al. [6]. Table 1 shows some of

the work done related to the analogy among others used in

supply chain context. These analogies help in investigating

the supply chain from a different perspective. However, as

mentioned before, we examine the supply process using a

fresh and interesting approach, that is, the vibrations

analogy.

3.1 Basic terminology

Any motion that repeats itself after an interval of time is

called vibration. Examples from common life include

swinging of a pendulum and plucked string of a guitar. The

theory of vibrations deals with the study of oscillatory

motion of bodies and the forces associated with them [20].

As shown in Fig. 2, a vibratory system in general

comprises:

(i) A means for storing potential energy, which may be

provided in the form of a spring or any other elastic

member.

(ii) A means for storing kinetic energy, which may be in

the form of mass or any other inertial member.

(iii) A means by which energy is gradually lost, which

may be provided in the form of a damper.

Presently, we are considering damped vibration system

with single degree of freedom. Further damping can be

classified in different ways such as:

(i) Coulomb or dry friction damping

(ii) Viscous damping

(iii) Hysteretic damping

Coulomb or dry friction as well as hysteretic damping

relate to the friction and therefore may not have direct

relevance for the present case. Further, viscous damping is

commonly considered in the vibration analysis. Also

because of its relevance, the viscous damping has been

used in the present paper after providing a brief overview

of the vibration.

The description as given in Table 2 forms the basis of

vibrations in the ‘‘vibration–supply chain analogy.’’ Before

moving on to the analogy, it is imperative to have a basic

idea of supply chain management/processes.

3.2 The supply chain management–vibrations analogy

According to APICS (APICS Dictionary [2], supply chain

management can be defined as ‘‘The design, planning,

execution, control, and monitoring of supply chain activi-

ties with the objective of creating net value, building a

competitive infrastructure, leveraging worldwide logistics,

synchronizing supply with demand, and measuring per-

formance globally.’’ According to the Council of Supply

Chain Management Professionals (CSCMP), ‘‘Supply

Chain Management encompasses the planning and man-

agement of all activities involved in sourcing and pro-

curement, conversion, and all logistics managementFig. 2 Fundamental elements of a vibratory system

Table 1 Some of the research work done in supply chain situation

Topic Author Area of study

How can fluid dynamics help supply chain management? Romano

[21]

Configuration of supply networks and business processes to achieve

time performance using fluid dynamics–supply chain analogy

Dynamic modeling and control of supply chain systems: A

review

Sarimveis

et al. [24]

Use of control theory approach in supply chain management

Application of control theoretic principles to manage

inventory replenishment in a supply chain

Sourirajan

et al. [28]

Use of control theoretic principles to manage the inventory

replenishment process in a supply chain under different forecast

situations

Measuring endogenous supply chain volatility: Beyond

the bullwhip effect

Kim &

Springer

[11]

Exploring the causes of supply chain volatility

6 Logist. Res. (2013) 6:3–15

123

activities.’’ It is the flow of material, money and informa-

tion starting from raw material supplier to the end

consumer.

As shown in the Fig. 3 [3], in any organization or any

business environment, purchasing, production and distri-

bution combine to form internal supply chain, whereas

maintaining cordial and mutually profitable relations with

suppliers is known as supplier relationship management.

While maintaining such relations at the customer end is

known as customer relationship management.

The basic objective of the supply chain is to make

available the right product, at the right time, in right

quantity, of right quality, at right place and more impor-

tantly at right price. But there are always some supply and

demand constraints that hinder achieving the aforesaid

objective. This paper focuses on analyzing the relationship

between the ‘‘design and critical design parameters’’ of

supply networks and its ability to dampen unwanted and

avoidable demand volatilities. A supply chain–vibrations

analogy as discussed in Table 3 has been developed to

understand the above relationship more clearly. As men-

tioned in Sect. 1, specific reasoning might be required for

agricultural products as compared to industrial products

and situations. Presently in the onion case, stock volume is

of less relevance in the context of shortages. This is

because of certain difference from the ‘‘industrialized’’

settings as discussed before. Due to shortages at the

extreme upstream, possibility of timely keeping more

generous stocks by the agencies becomes less relevant.

Further, because of the very nature of product and process

characteristics, information sharing appears to contribute to

the damping in a significant manner. Therefore, the

damping ability of this kind of supply chain is an essential

parameter in the present case.

From the above discussion, it is clear that the basic

properties of a vibratory system (stiffness and damping)

resemble the supply chain parameters. Moreover, viscous

damping deserves more elaboration here as it resembles the

supply chain environment to a large extent.

3.3 The concept of viscous damping

Viscous damping is the most commonly used damping

mechanism in vibration analysis. When mechanical sys-

tems vibrate in fluid medium such as air, gas, water, and

oil, the resistance offered by the fluid to the moving body

causes energy to be dissipated. Viscous damping is often

added to the mechanical system as a means of vibration

control. In the same way, the structural framework of a

supply chain acts as a means of vibration and fluctuation

control of demand. This aspect will be more clearly

explained through the case later.

Viscous damping is also characterized by damping

factor (n), which can be represented mathematically

as:.n ¼ ccc

.Here, ‘‘c’’ is the damping coefficient and ‘‘cc’’’ is

the critical damping coefficient, which ensures achieving

the approximately equilibrium position of a vibratory sys-

tem (1 degree of freedom) in minimum time [10].

This results in three cases of viscous damping:

Fig. 3 A general supply chain

Table 2 Typical characteristics of spring damper system

S. No Spring (refer Fig. 2) Viscous damper

1. It is connected at both ends with mass on one side and rigid

surface on the other

Viscous damping occurs in a mechanical system because of viscous

friction that results from the contact of a system component and a

viscous liquid

2. Its one end is fixed and the other moves with movement of

mass triggered by initial displacement from mean position

The damping force is produced when a rigid body is in contact with a

viscous liquid and is usually proportional to the velocity of the body

3. Stiffness (k) is the basic mechanical property of a spring Damping coefficient (c) is the specific characteristic of a viscous damper

as shown in Fig. 2

Logist. Res. (2013) 6:3–15 7

123

3.3.1 Underdamped system with n\ 1

In a viscously damped system, once free oscillations

commence, the non-conservative viscous damping force

continually dissipates energy. The system oscillates about

an equilibrium position, but each time it crosses equilib-

rium position, the system’s total energy level is less than

that in the previous time. The system oscillates with fre-

quency lower than natural frequency of the system, and it is

called ‘‘frequency of damped vibration.’’ Also, the ampli-

tude of vibration decreases exponentially with time, and

thus the system will take infinitely long time to be stable at

its mean position as depicted in Fig. 4a.

3.3.2 Overdamped system with n[ 1

The free vibration response of an overdamped system of

one degree of freedom is aperiodic, and the response decays

after reaching a maximum [refer Fig. 4b]. In this case also,

the system will take long time to attain equilibrium position.

3.3.3 Critically damped system with n = 1

In a critically damped system, the damping force that

leads to critical damping dissipates entire energy of the

system before one cycle of motion is complete. A critically

damped system can thus pass through equilibrium at most

once before the motion decays. Hence, critically damped

system brings back the system to nearly equilibrium posi-

tion in the shortest time, which is evident from Fig. 4c.

From the above discussion, we can see that the damping

coefficient (c) plays a major role in deciding the type of

damping that will occur in viscous damping of a single

degree of freedom system. Similarly, the damping ability

of a supply chain decides about the type of damping or

subsequently the time required to dampen the fluctuated

demand or to bring it back to nearly equilibrium level.

The detailed interpretation of damping coefficient (c) or

the damping ability of the supply chain can be made pos-

sible with the help of a viscous damper or a simple dashpot

model.

The damping coefficient (c) of a simple dashpot can be

given as:

c ¼ lA

h

In the above equation, ‘‘l’’ represents the dynamic vis-

cosity of fluid in the reservoir or dashpot. ‘‘A’’ represents

the area of plate in contact with fluid. The plate slides over

the fluid in the dashpot, which in turn provides resistance or

damping to the motion of plate. ‘‘h’’ represents the depth of

reservoir or dashpot.

3.4 Viscous damping applied to supply chains

In terms of supply chain, the interpretation of the above

parameters is as follows:

3.4.1 Critical damping coefficient (Cc)

In terms of supply chain, it can be interpreted as the critical

damping ability of a supply chain which can bring back the

fluctuated demand to nearly equilibrium state in minimum

possible time.

3.4.2 Dynamic viscosity (l)

In fluid dynamics, l depends on the degree of interaction or

strength of interaction between the fluid particles. In terms

of supply chain, it can be easily viewed as the degree of

Table 3 Vibrations analogy

S. No Vibrations Supply chain

Spring

1. It is connected at both ends with mass on one side and

rigid surface on the other

Supply chain also has two ends, that is, supply and demand, with supply side

mostly acting as rigid surface due to capacity constraint (supply disruption

may still occur at an intermediate stage despite the capacity constraint at an

extreme end)

2. The non-fixed end moves with movement of mass

triggered by initial displacement from mean position

Demand gets fluctuated from mean position or orders get volatile due to

disruption in supply side

3. Stiffness (load required to produce unit deflection) is the

basic mechanical property of a spring

Stiffness in a supply chain can be viewed as the ability of supply chain to

bear the supply shock without posing the stock out situation to the

customers

Viscous damper

1. Damping occurs between parts due to interaction or

friction of system component and viscous liquid

Damping of volatile demand may be achieved, if there is necessary and

enough interaction or information sharing within and between channel

partners

2. Damping coefficient (c) is the specific characteristic of

any viscous damper

Damping ability of supply chain may soon become a quintessential

parameter while describing a supply chain

8 Logist. Res. (2013) 6:3–15

123

interaction or information sharing within and across the

different tiers of a supply chain. In practice, it might be

difficult to quantify the degree of interaction or the level of

information sharing. But a qualitative judgment is possible

concerning an appropriate or optimum level of information

sharing after experiencing the disadvantages of low and

high level of this parameter. If the different links of a

supply chain do not interact among and across different

tiers of a supply chain or if the information sharing is very

low among them, then the orders may get inflated at each

stage. Thus, it may take very long time to dampen order

volatility, and a state of underdamped vibration may arise.

On the other hand, if information sharing is too strong

between two members of a supply chain, then the reaction

of one member may be so fast to even a small supply

disruption at its upstream member that it may lead to

inflated orders or increase in order volatility within a

supply chain. Thus, we need an optimum l or the strength

of interaction and information sharing among the members

of a supply chain.

3.4.3 Area (A)

‘‘A’’ represents the area of plate in contact with fluid in a

simple dashpot model. In terms of supply chain, ‘‘A’’ can

be represented as the number of suppliers or members of

supply chain in a tier. If the number of suppliers at each

stage is low, then it increases the dependency of complete

supply chain on one or few members, which may result in

inflated orders due to fear of rationing. This particular

(a) Damping Behaviour of an underdamped system

(b) Damping Behaviour of an overdamped system

(c) Damping Behaviour of a critically damped system

Fig. 4 Damping behavior

Logist. Res. (2013) 6:3–15 9

123

aspect is also supported by the literature, as many

researchers have found existence of inflated demand in fear

of rationing by suppliers. On the other side, if the number

of suppliers at each stage or tier is very high, then it may

lead to an increase in complexity of supply chain, which

further reduces the damping ability of the supply chain.

Thus, we need an appropriate or optimum number of

suppliers at each stage or in a tier to attain the state of

critical damping, which dampens the order volatility to

equilibrium in minimum possible time.

3.4.4 Depth (h)

In a simple dashpot model, ‘‘h’’ represents the depth of

liquid to which the fluid is filled. In the supply chain

analogy ‘‘h’’ can be viewed as the mean distance between

suppliers in any tier or stage of a supply chain. The term A

(Area) ensures that there should be optimum number of

suppliers in a tier whereas ‘‘h’’ further puts a check that the

mean distance between any two suppliers should also be

appropriate or optimum. When h is optimum, that is, the

mean distance between suppliers is optimum, then the

dependency on few suppliers gets reduced, and thus, vol-

atile and fluctuated demand can be easily dampened, which

comes as aftershock of supply disruption. However, if ‘‘h’’

is too small, then it may lead to an unnecessary increase in

complexity of supply chain, which may lead to over-

damped condition. Similarly, if ‘‘h’’ is very large (an

indication of comparatively lower number of suppliers),

then it may increase the dependency on one or few

suppliers, which may take long time for dampening fluc-

tuated demand, thus resulting in underdamped state of

vibration.

From the above discussion, it can be easily concluded

that the three parameters of a supply chain structure (l, A,

h) decide the type of damping that may occur in a supply

chain and the time that a supply chain takes to dampen the

fluctuated and volatile demand after a supply shock or

disruption. An interaction among these parameters is pos-

sible. For example, a very large ‘‘h’’ might indicate a lower

number of suppliers comparatively. However, a relation-

ship of substitutability between number of suppliers and

mean distance between suppliers cannot be established

precisely in general. For instance, a large number of sup-

pliers do not necessarily reveal smaller mean distance

concerning each end consumer. Such consumer may not

switch to more distant supplier after getting relevant

information. There is a need to critically examine the

parameters separately, and a combination of qualitative and

quantitative aspects varies from case to case. This can be

understood more clearly with the help of an analysis of the

case of onion supply, that is, the crisis during 2010–2011.

4 Case analysis

Like a general supply process of food chain, onion is also

reaching to the consumers through several channels. This

section describes the following:

(i) Various tiers in the supply process of onion

(ii) Supply chain–vibrations analogy in the present case

4.1 Tiers in the supply process of onion

As shown in the Fig. 5, the onion supply chain mostly

comprises five tiers:

(i) Tier I: This forms the basis of the onion supply chain

and sometimes also called the primary source. This

mainly includes the production of onion in farms.

Other source of supply in this tier includes importing

the onion. However, as India is one of the largest

producers of onion in the world, it generally exports.

(ii) Tier II: This includes channel partners that perform

the activities like processing, grading and packing

and thereby add value to the supply chain as a whole.

These are generally located near the farms where

onion crop is cultivated. The channel partners of this

tier are also involved in the export of onion as per

norms laid by the government.

(iii) Tier III: Agrimandis are agrimarkets constituting a

significant constituent of tier III of the onion supply

case. This includes the channel partners that store the

supply received from the tier II partners and fulfill

the demand of downstream members. This is the

most critical link in the entire supply chain as

aggregation and disaggregation of demand in the

form of order takes place here. Their location,

distance among them, storage capacity and their

interaction within and among the tier is of prime

importance, which decide the overall stiffness and

damping capacity of the supply chain. This is more

clearly elaborated later.

(iv) Tier IV: This includes channel partners that deal

directly with customers, that is, retailers. These act as

the source of information located at the customer end

for its demand, preferences, traits, etc.

(v) Tier V: This comprises end customers finally. The

customers vary demographically, geographically,

economically and socially which get reflected in their

buying or ordering behavior.

Although all tiers are important for proper functioning

of the complete supply chain, but tier III is the most critical

among all, as it performs the function of aggregating as

well as disaggregating. It aggregates the supplies from tier

10 Logist. Res. (2013) 6:3–15

123

II, which constitutes graders, packers and traders, and di-

saggregates among tier IV and tier V.

4.2 Understanding the onion crisis through supply

chain–vibrations analogy

As per data collected from the National Horticulture Board

portal, 34 agrimarkets (agrimandis) supply the onion to all

the states and union territories of India. These agrimandis

constitute tier III of the onion supply chain in India. The

location of agrimandis is depicted in the Fig. 6.

As shown in Fig. 6, the number of agrimandis (A) is not

enough to cover the entire country, that is, the number of

suppliers in tier III are few. This increased the dependency

of supply chain on few suppliers and left the tier IV and tier

V customers with few options to fulfill their demand. It

resulted in inflated demands during crisis due to fear of

rationing, which consequently increased the time to bring

the prices back to normal. From the vibrations analogy, low

value of ‘‘A’’ leads to the situation of underdamped

vibration, which means that the system will need indefi-

nitely long time to achieve equilibrium.

Also, the mean distance between the agrimandis (h) is

too large, which leads to dependency of tier IV and tier V

on few suppliers (agrimandis) in tier III, which again

resulted in inflated orders during supply disruption leading

to long time for price recovery. From the vibrations anal-

ogy, also high value of ‘‘h’’ leads to underdamped vibration

and consequently will need a long time to achieve

equilibrium.

The degree of interaction or the information sharing

among agrimandis (l) and with its up and downstream is

negligible. Wherever present, the communication is not

effective enough due to reluctant attitude of traders. This

factor again contributed to the onion crisis during

December 2010–January 2011.

For getting more insight into the case, we have focused

our study on two clusters, which behaved differently during

the onion supply crisis. The first cluster comprises two

states, namely Maharashtra and Gujarat, which share

common border in the Union of India. The second cluster

comprises another two states, namely Punjab and Haryana,

and one Union Territory, that is, Chandigarh. The study has

been done for the same commodity (onion) and for the

same time period (December 2010) and the data used are

captured from the website of the National Horticulture

Board, India (www.nhb.gov.in) [16].

4.2.1 Cluster 1: Maharashtra and Gujarat

In this cluster, there are seven agrimandis, which both

serve the states and form tier III of the onion supply chain.

In terms of vibrations analogy, it represents ‘‘A,’’ which is

the number of suppliers in a tier of supply chain. In total,

they serve a population of 173 million people living in an

area of 504,024 km sq. Thus, the area density of agrimandi

in this cluster is 72,003 km sq per agrimandi. The average

distance between two agrimandis in cluster 1 is 403 km,

which represents ‘‘h’’ in the vibrations analogy. Few agri-

mandis in the cluster and high average distance between

the agrimandis acted as a resistance for information sharing

among and across the members of a tier in a supply chain.

In terms of vibrations analogy, it (i.e., resistance created

due to ‘‘h’’ and ‘‘A’’) has reduced the degree of information

sharing (l) in the supply chain. In this way, all the three

factors (l, A, h) had led the market to the underdamped

situation when the supply got disrupted in December 2010–

January 2011.

Fig. 5 Channels in the onion

supply

Logist. Res. (2013) 6:3–15 11

123

4.2.2 Cluster 2: Punjab, Haryana and Chandigarh

In this cluster, the five agrimandis serve the two states and

a union territory to form tier III of the onion supply chain.

Thus, the number of suppliers in a tier (A) is five. These

serve people living in an area of 94,574 km sq. The area

density of agrimandi in this cluster is calculated to be

18,914 km sq per agrimandi and the average distance

between two agrimandis (h) as 226 km. Unlike cluster 1,

adequate number of agrimandis and relatively low average

distance between two agrimandis help in better information

sharing and coordination (l) in the supply chain.

4.2.3 Comparing Cluster 1 and Cluster 2

Figures 7 and 8 represent the study done for the period during

which the onion supply crisis occurred, and thus, the study

takes into account only the number of trading days in that

particular month, that is, December. Also the start and end of

the damping period are decided on the basis of fluctuations in

price and arrival quantity. The damping period is considered

‘‘start’’ when price and quantity fluctuate simultaneously and

‘‘end’’ when both attain nearly equilibrium state with low

fluctuations. From the above discussion, we find that in case of

the supply disruption, all the three parameters of the vibrations

analogy enable the cluster 2 to dampen the order volatility in

lesser time as compared to the cluster 1. This is evident from

Figs. 7 and 8, where price and arrival both have been shown

on the basis of available data.

After analyzing all the three factors from the current

case perspective, it can be easily concluded that these

factors might lead to the situation of underdamped/criti-

cally damped vibration in a supply chain, and it took some

time to bring the situation back to normal. However, in

practice, the cases are analyzed relatively. A comparison is

also shown in Table 4 for the cluster 1 and cluster 2.

Because of the combination of parameters, cluster 2 seems

to handle the situation relatively better.

In practice, a case comparison method has often proved to

be useful. The present case helps in understanding the overall

system behavior better with the use of vibrations analogy. The

approach is suitable for certain generalization also. For

instance, if a supply system is found to be underdamped, then

the damping coefficient is lower than its critical value. In order

Fig. 6 Spread of agrimandis in

India

12 Logist. Res. (2013) 6:3–15

123

to improve the situation, the management practice needs to

focus on the following parameters:

(i) Degree of interaction or information sharing

(ii) Number of suppliers in a tier

(iii) Mean distance between suppliers

In the real world scenario, the managerial attention

could be directed toward one or more parameters. For

rigorous quantification, suitable relevant combination of

parameters [30, 32–34] in the context of more complex

multi-item scenario might also be considered depending on

the degree of efforts needed to improve them.

5 Conclusion

In the context of vibration theory, the critically damped

system will reach the equilibrium position in the shortest

Fig. 7 Cluster 1: monthly price

and arrival report (Nagpur

Mandi, December 2010)

Fig. 8 Cluster 2: monthly price

and arrival report (Amritsar

Mandi, December 2010)

Table 4 Parameter comparison for Cluster 1 and Cluster 2

S. No Parameter Cluster 1 (Maharashtra

and Gujarat)

Cluster 2 (Punjab

and Haryana)

1 Number of agrimandis in a cluster 7 5

2 Average distance between two agrimandis in a cluster (km) 403 226

3 Average area covered/agrimandi (km sq) 72,003.43 18,914.8

4 Average no. of people served/agrimandi (million) 24.67 10.82

5 Degree of information sharing Low Relatively high

6 Time taken to dampen order volatility during crisis 11–15 days 6–8 days

Logist. Res. (2013) 6:3–15 13

123

time. This happens when the damping coefficient reaches

the critical value. Further, the damping coefficient is

expressed in terms of viscosity, area and depth. Relying on

the vibrations analogy, these terms are explained in the

supply chain situation. Ideally, the combination of these

relevant parameters must be such that any supply distur-

bance can be handled in the shortest possible time. In order

to understand the phenomena, an onion supply case has

been analyzed. A relative comparison is useful in investi-

gating the interaction of various parameters concerning a

supply case, and this comparison has been shown clearly.

In the present case, cluster 2 performed well because of an

appropriate level of (i) mean distance between agrimandies,

(ii) average area covered/agrimandi and (iii) degree of

information sharing. In order to generalize the findings,

damping coefficient needs improvement if underdamping is

observed in the supply system by a manager. For analyzing

the situation, following questions should be explored:

(i) Is there any scope for enhancing the degree of

information sharing?

(ii) Is there any possibility to increase the number of

suppliers in a tier?

(iii) Should the mean distance between suppliers be

reduced?

Generally speaking, this situation can be improved by an

increase in the number of suppliers in a tier and degree of

interaction, along with a decrease in the mean distance

between suppliers. However, there are supply system

constraints in practice and thus suitable option or a com-

bination of suitable options should be focused and imple-

mented. Further, the proposed methodology needs to be

tested for other business sectors as well. Concerning the

case-specific environment, additional parameters might be

included to explain the supply system behavior better.

References

1. Arshinder K, Kanda A, Deshmukh SG (2008) Supply chain

coordination: perspectives, empirical studies and research direc-

tions. Int J Prod Econ 115:316–335

2. Blackstone Jr. JH, Jonah J (2008) APICS dictionary, 12th edn,

134

3. Chen IJ, Paulraj A (2004) Towards a theory of supply chain

management: the constructs and measurements. J Oper Manag

22(2):119–150

4. Chopra S, Sodhi MS (2004) Managing risk to avoid supply-chain

breakdown. MIT Sloan Management Review, Fall, pp 53–61

5. Croson R, Donohue K (2006) Behavioral Causes of the Bullwhip

Effect and the Observed Value of Inventory Information. Manag

Sci 52(3):323–336

6. Dejonckheere J, Disney SM, Lambrecht MR, Towill DR (2003)

Measuring and avoiding the bullwhip effect: a control theoretic

approach. Eur J Oper Res 147:567–590

7. De Treville S, Shapiro RH, Hameri AP (2004) From supply chain

to demand chain: the role of lead time reduction in improving

demand chain performance. J Oper Manag 21:613–627

8. Disney SM, Towill DR (2003) Vendor-managed inventory and

bullwhip reduction in a two-level supply chain. Int J Oper Prod

Manag 23(6):625–651

9. Kachani S, Perakis G (2006) Fluid dynamics models and their

applications in transportation and pricing. Eur J Oper Res

170:496–517

10. Kelly SG (2000) Fundamentals of Mechanical Vibrations, 2nd

edn. Singapore, Mc Graw Hill

11. Kim I, Springer M (2008) Measuring endogenous supply chain

volatility: beyond the bullwhip effect. Eur J Oper Res

189:172–193

12. Lai KH, Wong CWY, Cheng TCE (2006) Institutional isomor-

phism and the adoption of information technology for supply

chain management. Comput Ind 57(1):93–98

13. Lee HL, Padmanabhan V, Whang S (1997a) The bullwhip effect

in supply chains. Sloan Manag Rev, Spring, pp 93–102

14. Lee HL, Padmanabhan V, Whang S (1997) Information distortion

in a supply chain: the bullwhip effect. Manag Sci 43(4):546–558

15. Lee HL, So KC, Tang CS (2000) The value of information

sharing in a two-level supply chain. Manag Sci 46(5):626–643

16. National Horticulture Board website www.nhb.gov.in, accessed

during Feb–Aug. 2011

17. Ozer O, Zheng Y, Chen K-Y (2011) Trust in forecast information

sharing. Manag Sci 57(6):1111–1137

18. PHD Chamber, Press Release; 30 Dec (2010) Price fluctuations,

supply chain management need to be monitored to check food

inflation

19. Prakash D, Shrotriya GC (2007) Enhancing the pungency through

‘‘Pink Revolution’’ -Marketing of onion in India. Rural Devel-

opment and Management Centre, New Delhi

20. Rao SS (2000) Mechanical vibrations, 2nd edn. Addison-Wesley

Publishing Company, Boston

21. Romano P (2009) How can fluid dynamics help supply chain

management? Int J Prod Econ 118:463–472

22. Rong Y, Shen Z-JM, Snyder LV (2008) The impact of ordering

behavior on order-quantity variability: a study of forward and

reverse bullwhip effects. Flex Serv Manuf J 20:95–124

23. Rong A, Akkerman R, Grunow M (2011) An optimization

approach for managing fresh food quality throughout the supply

chain. Int J Prod Econ 131:421–429

24. Sarimveis H, Patrinos P, Tarantilis CD, Kiranoudis CT (2008)

Dynamic modelling and control of supply chain systems: a

review. Comput Oper Res 35:3530–3561

25. Saeed KA, Malhotra MK, Grover V (2005) Examining the impact

of interorganization systems on process efficiency and sourcing

leverage in buyer–supplier dyads. Decis Sci 36(3):365–396

26. Sanders NR, Premus R (2005) Modeling the relationship between

firm IT capability, collaboration, and performance. J Bus Logist

26(1):1–23

27. Schleifenbaum H, Uam J-Y, Schuh G, Hinke C (2009) Turbu-

lence in production systems: fluid dynamics and its contributions

to production theory. Proceedings of the world congress on

engineering and computer science Vol II WCECS 2009, October

20–22, 2009, San Francisco, USA

28. Sourirajan K, Ramachandran B, AN L (2008) Application of

control theoretic principles to manage inventory replenishment in

a supply chain. Int J Prod Res 46(21):6163–6188

29. Sharma S (2008) On the flexibility of demand and production

rate. Eur J Oper Res 190(2):557–561

30. Sharma S (2008) Theory of exchange. Eur J Oper Res

186(1):128–136

31. Sharma S (2009) A composite model in the context of a pro-

duction-inventory system. Optim Lett 3(2):239–251

14 Logist. Res. (2013) 6:3–15

123

32. Sharma S (2009) Extending Sanjay Sharma’s theory of exchange.

Int J Appl Manag Scince 1(4):325–339

33. Sharma S (2009) Single/multiple parameter swapping in the

context of Sanjay Sharma’s Theory of Exchange. Int J Adv

Manuf Technol 40(5-6):629–635

34. Sharma S (2009) A method to exchange the demand of products

for cost improvement. Int J Adv Manuf Technol 45(3-4):382–388

35. Sharma S (2010) Policies concerning decisions related to quality

level. Int J Prod Econ 125(1):146–152

36. Sharma S, Dubey D (2010) Multiple sourcing decisions using

integrated AHP and knapsack model: a case on carton sourcing.

Int J Adv Manuf Technol 51(9-12):1171–1178

37. Sharma S (2011) Effects concerning quality level with the

increase in production rate. Int J Adv Manuf Technol 53(5-8):

629–634

38. Sharma S (2012) Development of supplier relationship including

cost of defectives in the cyclic production. Prod Plan Control

Manag Oper. http://dx.doi.org/10.1080/09537287.2012.666866

39. Van Donk DP, Akkerman R, Van der Vaart T (2008) Opportu-

nities and realities of supply chain integration: the case of food

manufacturers. Br Food J 110(2):218–235

40. Vonderembse MA, Uppal M, Huang SH, Dismukes JP (2006)

Designing supply chains: towards theory development. Int J Prod

Econ 100:223–238

41. Yang J, Wong CWY, Lai KH, Ntoko AN (2009) The antecedents

of dyadic quality performance and its effect on buyer–supplier

relationship improvement. Int J Prod Econ 120:243–251

Logist. Res. (2013) 6:3–15 15

123